1. A particle moves on a given straight line with a constant speed v. at a certain time it is at point P on its straight line path. O is a fixed point. Show that vectorOP × vectorv is independent of the position P.

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- Dec 3rd 2006, 06:20 AMvritikaguptaplease help with vectors
1. A particle moves on a given straight line with a constant speed v. at a certain time it is at point P on its straight line path. O is a fixed point. Show that vectorOP × vectorv is independent of the position P.

- Dec 3rd 2006, 09:57 AMCaptainBlack
Every point on the path of the particle may be written:

$\displaystyle \bold{p}=\bold{p_0}+\bold{v}t$,

where $\displaystyle \bold{p_0}$ is the position of the particle at $\displaystyle t=0$.

Then:

$\displaystyle \bold{p}\wedge \bold{v}= (\bold{p_0}+\bold{v}t) \wedge \bold{v}

=\bold{p_0}\wedge \bold{v}+(\bold{v} \wedge \bold{v})t=\bold{p_0}\wedge \bold{v}

$

which is independent of $\displaystyle t$, and so of the particular point $\displaystyle \bold{p}$.

RonL